Twisting Elements in Homotopy G-algebras

We study the notion of twisting elements $da=a{\cup }_{1}a$ with respect to ${\cup }_1$ product when it is a part of homotopy Gerstenhaber algebra structure. This allows to bring to one context the two classical concepts, the theory of deformation of algebras of M. Gerstenhaber, and $A(\mathrm{\infty })$-algebras of J. Stasheff.